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The anomalies which have occurred in the measures of degrees, and of which the appearances seem to increase in proportion as greater pains are taken to avoid inaccuracy, have naturally drawn the attention of mathematicians; and the question, what part of them is to be ascribed to error, and what to irregularities in the structure of the globe, has come, of course, to be considered. That a small part of them only can be ascribed to the former cause, is rendered probable by the very circumstance just stated; that they are not diminished, nay, that they even seem to be increased, by the care taken to avoid error. It seems clear, from that consideration, that the irregularities are in the object sought for, and are only brought more in sight by more microscopical observation, by the excellence of the instruments, the accuracy of the computations, and the extent of the lines measured. No measurement was ever executed with greater care than that in France; and the great extent of the arch measured, as well as the ability and skill of the observers, make the mean result, the length of the degree in the parallel of 45°, the datum most perfectly ascertained of any that regards the figure of the earth. Yet even here, we find in the
ought to be diminished by the sum of all these quantities before it is divided by the amplitude; and this division gives not the degree in the middle of the arch, but that at the beginning of it, or the farthest to the south.
detail that there are great anomalies, and that the successive degrees increase with much irregularity.
The arch between Greenwich and Dunkirk gives the degree greater than that which is derived from the arch between Dunkirk and the Pantheon at Paris by 7.23 toises; the next difference is 8.4; then 32.4, 12.9; and lastly-2 from the arch between Montjouy and Formentera. In this last case, there is an absolute retrogradation; and the degree increases on going to the south, just as it is observed to do in the arch measured in England, and in that measured in Hindostan.
The irregularities in the French measurement induced Delambre to scrutinize the latitudes of all the above places with the utmost care; but he could find nothing sufficient to account for the irregularities. (See Base Métrique, Tom. III. p. 84.) The observation of the latitude at Montjouy appeared exact; yet, when compared with one at Barcelona, very near to Montjouy, an error of 8".24 was discovered; and Delambre, apparently with much reason, considers this difference as a certain proof of the irregularities of the earth. To the same cause he ascribes the rest; and, indeed, from the very progress which they hold, some local affection seems necessarily suggested.
The consequence of all this is, that for the whole of the arch in France, the degrees are best represented by supposing a compression of, or
; while, by taking in a greater range, and comparing the degrees in France with those in distant countries, the compression comes out less than the half of this, viz., or. To reconcile the measures actually made with a compression of 20 it will be necessary to make the following corrections on the latitudes :-For Paris, 0; Montjouy, +3′′.6; Carcassonne, + 0.88; Dunkirk, + 3′′.06; and for Evaux, +5′′.83. These are wholly improbable as errors of observation, and must be attributed to local attractions, which act irregularly on the plumb line.-Bâse Mètrique, ib. p. 92.
The same thing may be said of the arc measured in England by Colonel Mudge: the whole arc, taken together, agrees very well with the measures in France, and with that in Lapland, as lately ascertained by the Swedish academy. * But if the parts of this
* We have compared together the five arches of the meridian, which, from their extent, and all other circumstances, seem the best entitled to confidence, viz. that in Peru, by Bouguer and Condamine; in Hindostan, by Major Lambton; in France and England, comprehending the whole extent, from the parallel of Greenwich, to that of Formentera, by Delambre and Mechain, and in part by General Roy; that in England afterwards, by Colonel Mudge; and, lastly, that in Lapland, by M. Swanberg; and the results which we have found are extremely consistent, and give, for the compression at the poles, 12.5. When this compression is adopted, there does not appear an error of more than 9 fathoms in the measure of any of the above degrees, The
arc be compared, an irregularity is found, and the degrees appear to increase on going from the north to the south. In giving an account of Colonel Mudge's measurement in a former Number of this Journal, we ascribed the fact just mentioned, to local irregularities in the direction of gravity, and we still consider this as by far the most probable supposition. A paper, however, written with great knowledge of the subject, and full of sound mathematical reasoning, has been published by Don Rodriguez in the Philosophical Transactions for 1812, which is quite on the opposite side, and ascribes the irregularities in the arc to errors of observation. Don Rodriguez, if we mistake not, is one of two Spanish gentlemen who accompanied MM. Biot and Arago, and assisted in the operations by which the meridian that had been traced through France was extended to the southernmost of the Balearic Isles. He seems perfectly acquainted with the methods of calculation, and all the most recent improvements which respect the problem of
French, from their own measures in France and Peru, bring out a compression of nearly. Thus the results are consistent with the supposition that the earth is an elliptic spheroid, when the arches compared are large and distant from one another: when they are small, and near to one another, they do not agree with that hypothesis, nor indeed with any other single hypothesis that can be laid down. This is what might be expected, and does not invalidate the general conclusion.
the figure of the earth. We do not think that he has proved that the irregularities in this measurement arise from errors of observation; and we are of opinion, though the amount of these irregularities may now be more exactly estimated than before, that with regard to their cause, the question rests precisely where it did. But though we are not convinced by Don Rodriguez, we must do him the justice to say, that his argument is fairly conducted, and that he has displayed great knowledge of the subject, and perfect familiarity with the best methods hitherto employed in the solution of this difficult problem. We have therefore observed with regret, that this ingenious foreigner has been attacked in some of the English Journals, with a violence and asperity which the subject did not call for, and which his paper certainly did not authorize.
When there are unlooked-for results in any system of experiments or observations, the errors into which the observer may have fallen, naturally come to be considered as affording one solution of the difficulty. We are not to suppose, that any man engaged in experimental investigations, can be exempted from such an inquiry; nor, when such inquiry is instituted, are we to suppose that he is subjected to a personal attack. The principle on which Don Rodriguez proceeds, though it may be erroneous, seems to be general; it is applied equalD d